How to get a better HDRI render?
Have you tried experimenting with different HDRIs? It could just be that the lighting you're getting from that specific HDRI isn't what you're looking for. If you want crisp shadows then maybe try looking for an HDRI that has a strong, single light source.

This is more anecdotal, but I've personally never had to put an HDRI at anything above a 2 in strength. This seems to lend more evidence to the HDRI itself being washed out/being the problem child